Swarm Intelligence–inspired Adaptive Routing Construction in WSN

Ru Huang1

School of Information Science & Engineering East China University of Science and Technology

Shanghai, China

Guanghui Xu2 Institute of Communications Engineering

PLA Univ. of Sci. & Tech. Nanjing, China

E-MAIL: huangrabbit@ecust.edu.cn

Abstract—The paper presents a heuristic Theoretical Optimal Routing Algorithm(TORA) to achieve location-aided optimal data-gathering structure in wireless sensor networks(WSN). The algorithm’s construction is based on a kind of swarm intelligence mechanism, i.e., ant colony optimization (ACO). The novel design of heuristic factor and pheromone updating rule can endow ant-like agents with the ability of detecting the local energy status of networks to approach the theoretical optimal routing. Via the division of WSN into different functional regions and introduction of energy-efficient weight in heuristic factor, the criterion in routing selection can be adaptively adjusted based on asymmetric power configurations and consumption to improve the robustness of data-routing tree. Finally, simulation results show that the proposed routing scheme can contribute to minimize the total communication energy cost, meanwhile, to enhance the QoS- performance and energy-balance effect in data-gathering.

Keywords-WSN; Swarm intelligence; routing; energy efficiency

I. INTRODUCTION Data gathering is a critical operation in WSN for extracting

useful information from the operating environment to base station sink. Constrained by the limited and non-replenished energy resources, minimizing energy consumption is considered as a major performance criterion to provide maximum network lifetime in WSN. Technologies[1-2] applied to balance the energy dissipation in networks are accepted universally as a key factor for prolonging the lifetime. But without geographic information support, periodic low rate data flooding throughout the network will cost lots of energy. So many current researches[3-6] focus on energy optimizing location-aided routing protocols, which are with both low power and fault tolerance to compliment the above disadvantages by efficiently using geographic-aware information to limit the new route search to a smaller “request zone”, which is estimated according to the prior position and mobility information of destination., thus conserve more energy. However, the size of the “request zone” maybe too large if the obtained information is inaccurate. To solve the above problems, GPSR[7] is proposed to utilize greedy decisions forwarding perimeter-mode packets in a derived simple planar graph. However, the energy of those nodes on the planar graph should be depleted quickly for concentrated traffic on the promiscuous listening mode. The above routing problems can be proved as NP-hard. Swarm Intelligence, which is the emergent collective intelligence

of groups of simple agents, is an efficient way to solve the concerned problems. Swarm is a population of interacting individuals, which contributes to optimize some global objectives via collaborative operations. As an important research domain of Swarm Intelligence, ACO is a constructive meta-heuristic optimization method and has been successfully applied to energy-saving routing[8-10] construction in WSN by colony of ant-like agents concurrently and asynchronously build optimal solutions via applying a stochastic local decision policy which makes use of pheromone trails and heuristic information. But those swarm intelligent themes only put emphasis on the positive-feedback mechanism to iteratively search optimization and have made some modifications to fit different network types, which should not be satisfied for special characteristics of WSN. In our proposed algorithm, prior theoretical results can be combined with swarm intelligence-inspired mode to further enhance the energy-efficiency of routing construction in WSN.

The rest of the paper is organized as follows: in section II, a system model is proposed and explained; we analyze an optimal theoretical routing structure in WSN and address the detailed design procedure of TORA in section III; the simulation results and conclusion are in the last two sections.

II. SYSTEM MODEL Wireless Sensor Networks (WSN) can be represented by a

weighted undirected graph ( , , )G V E W= , where V and E respectively represent the set of nodes and links in G , while W denotes the set of weights with E G⊂ . Each link ,i j E< >∈ is associated with a delay parameter ,i j WDelay< > ∈ and the total

delay requirement for QoS is set as ThresholdD . In WSN, the energy consumption of sensors in network should be unbalanced for the reason of asymmetric traffic distribution in data flow. In the data-gathering routing rooted at sink, the energy cost of each sensor is related with its own locality hierarchy in the tree structure. If the sensor’s geographical position is closer to sink, its hierarchy in the tree structure and its corresponding energy cost is higher due to large amount of data aggregation. So we divide the WSN into three categories of functional regions according to the ER (event radius model) [11] with disparity in the energy cost caused by the unbalanced streams distribution. In ER

The work is supported by foundation project of State Key Laboratory for Novel Software Technology at Nanjing University (KFKT2009B18) and Science Foundation for the Excellent Youth Scholars at East China University of Science and Technology(YH0157127).

978-1-4244-3709-2/10/$25.00 ©2010 IEEE

model, events are sensed by a subset of nodes V Vs ⊂ , i.e. the

data-sensing region. The data-merging region V Vc ⊂ is defined

as a disk centered at sink with radius cricald denoting the critical

distance of 'Vc s boundary to sink. And the sensors in

V V V Vr s c= − ∪ compose the data-relaying region. It is assumed that each sensor node maintains a cache storing neighborhood’s information and self-address which is obtained by GPS and known by sink as a priori and each artificial kant ( 1, 2, ,k Vs= )has a memory kM , whose components are denoted as follows:

TABLE I. COMPONENTS DEFINITION IN kM

Component Definition

Distinguish ant agent from data packet.

Tabu list that records the path( )vL built by

artificial

Records the number of accumulated hops

Remaining energy level of

The current feasible neighborhood of kant is defined as ( )( )

KA ( )v iLV O−= ∩ , where ( )iO is the set of neighbors in in . Via the functional region division of sensor networks and the ability of ant’s memory, artificial ant can roughly estimate the energy-cost-level of each reached sensor and correspondingly adjust the weight in heuristic information of routing selection to improve the reliability of data-gathering tree.

Let ( ) ( )/lef inii i iR E E= denotes the remaining energy level of

i Vn∀ ∈ . The routing tree problem Ξ is defined to find a series

of optimal paths *{ } |treemult k kpath= from V Vs ⊂ to destination

sink subjected to the following conditions:

* *1( ) tree| ,k

hopi k i k multkn path path GR R path

couter ∈ ∀ ∈ ⊂≥∑ (1)

,,( )

k Thresholdi ji j pathkpathDelay Delay D< >< >∈= ≤∑ (2)

Where (1) and (2) are constraint conditions for QoS requirement of energy optimization and temporal consistency.

*( )kR path denotes the average remaining energy ratio of optimal path *

kpath . Ξ is also a NP-hard Constrained Path Optimization (CPO) problem and can be solved by Lagrange Multiplier

algorithm(LM). The Lagrange function is described as:

, , [ ]( ) ( )( )i ipath pathD Dpath DelayL Rλ λ −+= , 0,[ ]i ThresholdD D∈ (3) The solutions can be obtained via calculating the partial

differential of Lagrange function matrix. But it is not suitable for the resource limited sensor nodes in WSN. So in the following section we propose TORA algorithm to solve this primary problem Ξ with a fully distributed way in ACO approach.

III. DESIGN OF OPTIMAL ROUTING STRUCTURE

A. The design of heuristic factor

It is assumed that nv sV∀ ∈ sends l -bit message on multi-

hop way to sink, which requires ( )K 1v − relay nodes and thi hop distance is di . Based on first-order-radio-model[12], the energy

expended by relaying l -bit message over a distance di is

( , d ) (2 d )nelec amprelay i iE El lε= + × . Given d( ,sink)vn is the

distance between the source vn , [1,| |]sVv∈ and sink, while ( )K v denotes the number of theoretic hops from vn to sink. So

the total cost on path ,sinkvn is( )K

totali 1

P (d ) ( ,d )v

i relay iE l=

= ∑ ,

which can be proved as a strict convex function, and its minimal value is only obtained on the condition that each hop distance is equal to optim

( ) ( )Kd d( ,sink) /v vvn= according to Jensen’s

inequality. Then optimal hop-counts(see (4)) will be calculated by imposing the derivative operation, i.e., total KP (d )/ 0i∂ ∂ = .

1

2

( )nK ( )(int) d( ,sink)

(n 1)v

vnα

α=

− (4)

where 1α and 2α are the node energy parameters. We set vector ( )vℑ as the coordinate sequence of theoretical points, i.e., ( ) ( )={ , ( ), }v vn tℑ , ( )K[1, ]vt ∈ and the rectangular

coordinates of each theoretical point for totalmin.P is deduced as follows:

( ) ( ) ( ) sinkoptim optim

sink

( ) ( ) ( ) sinkoptim optim

sink

*cos[arctan ]

*sin[arctan ]

( ) *d

( ) *d

v v v vhop v hop

v

v v v vhop v hop

v

couter couter

couter couter

y yx xx xy yy yx x

−⎧ = +⎪ −⎪⎨ −⎪ = +⎪ −⎩

(5)

At ( )hop

jcouter , the distance-error between theoretical optimal sensor and actual counterpart is calculated by Eq.(6)

hopcouter

antid

pathk

iR i kpathn∀ ∈

antk

2 2optim optim

( ) ( ) ( ) ( ) ( )d ( )=[ ( )] [ ( ))]j v j v jj hop j hop j hopcouter couter couterx x y yΔ − + − (6)

Define triple ( , , )S B R H= as the current state obtained by ant agent for next hop selection, that is to say, during the process of routing building, ant takes the bias B , the remaining energy level R and the hop counts H into account. Let state vector

( , , )j j j jB R Hs S= ∈ , and each tuple of js is defined as follows:

( )d ( )jj j hopcouterB = Δ (7)

(lef) (ini)j jE E/jR = (8)

( )j hop

jcouterH = (9)

where jB provides the location-aided energy-efficiency information for the process of path building, which helps ant agent to adjust the forward direction to sink based on bias value.

jR shows the energy status of jn and jH denotes the hops of ant

agent to reach the source node s Vs∈ through node jn . With the accumulation of hop-counts, the probability of reached jn belongs to data-merging region Vc will also be increased and higher energy consumption will be expended consequently. Therefore, according to the distribution trait of energy cost in routing tree, we set the relationship between each tuple in S as (10), which indicates that the closer the current sensor to sink, the larger the weight of remaining-energy-level will be introduced into energy efficiency factor.

( ) /j j j jH R Bϖ = , KAjn∀ ∈ (10)

We also associate cost j Wϖ ∈ with each KAjn∀ ∈ as local evaluation information for node’s robustness. The higher the value of jϖ , the greater the probability of jn will be selected as the next hop node on the building of optimal routing path. If

Ken Aarg max { }jk ϖ∈= , then ant at current sensor in tends to

choose kn as the next hop sensor. So the structure of heuristic factor for ACO is designed as

ij jη ϖ= , KAjn∀ ∈ (11)

which embodies the idea that artificial ant can adaptively choose the high-energy-efficient sensor as its next hop for each step and correspondingly adjust the variable weight to improve the reliability of data-gathering tree. In two extreme cases, i.e., if

0jH = or (lef)E 0j = then 0ijη → , which indicates

that jn belongs to data-sensing region j Vsn ∈∀ , or it will run out of energy, then ant agent should abandon the selection of

jn in the path building.

B. Algorithm flow At the initial stage of TORA, the optimal routing tree, i.e.,

treemult is empty and each sensor in V Vs ⊂ takes sink as the common destination. sink instructs sensors in Vs to create ant-like agents for constructing optimal routing paths and compute the corresponding theoretic points sequence ( )vℑ . The above task is sent via ‘interest’, which also contains the address coordinate of sink, i.e., sink sink( , )x y , and propagated passed through the

network to Vs . The ant started from sensor v Vsn∀ ∈ is denoted

as forwkant , at each step, it chooses the next unvisited node in the

current feasible neighborhood with the improved transition probability given by (12) and constructs ( )path treev

mult∈ from source to sink, if it doesn’t meet any sensor which has been added to treemult ,

K

[ ( )] [ ]( )

[ ( )] [ ]A

tij ijP tij tm im im

βατ ηβατ η

=∑ ∈

(12)

When forwkant arriving at sink, the corresponding backward

ant, i.e., backkant is created and back along the built ( )path v to

nv , any sensor visited by backkant is set with a mark, which

denotes the sensor belongs to treemult . Meanwhile, backkant carries

path information copied from forwkant and deposits the

pheromone trails on the visited sensors according to

(1 )k k ki i iτ ρ τ ρ τ+− ⋅Δ← (13)

Where (0,1)ρ ∈ represents the volatility degree of pheromone.

Total energy remaining ratio i i in path R∈∑ and hopcouter carried

by forwkant will be used to update pheromone.

11( ) ( ) ( )

( )

[ ],

0 ,

kk i k k Thresholdi

Threshold

R path R path Delay k

Delay k

D

D

ττ

λ−−Δ −

Δ+ ≤

= >

⎧⎨⎩

(14)

According to the updating rule, pheromones of those sensors in treemult will be adaptively reinforced subjected to constraint

conditions (1) and (2) of Ξ . When backkant arrives at nv Vs∈ , it

dies and the optimal routing from nv to sink will be set up. On

the other case, if forwkant meets n treej mult∀ ∈ , it stops further

search to set the current graft sensor n j as destination and comes back to source for re-executing the above algorithm. The algorithm is over when all source sensors in Vs have been added

into treemult , which is composed by those corresponding optimal routing paths from each source sensor to sink. In TORA, we can also easily prove that the final routing tree structure is loop-free by using the tabu list in ant’s memory and the time-complexity of TORA has the linear relationship with the steps moved by artificial ants. According to the function connection between solution quality and steps, the optimal solution can be obtained by 2logk m steps and the time-complexity is deduced

as 2( log )O m mk .

IV. SIMULATION RESULTS The algorithm TORA has been simulated in a network of

adjustable-density sensors(25 ∼ 140) randomly distributed over a square of 500x500 units with the base station at (15, 480). The link layer is implemented using IEEE802.11 MAC protocol. Each sensor has a tunable communication radius

cξ ( c optim( )d vξ ≥ ). In the radio model, each radio dissipates

50 /elecE nJ bit= to run transmitter or receiver circuitry and 2100 / /amp pJ bit mε = for the transmitter amplifies. The

parameters in ACO are set as follows: 1α = , 5β = , 0.9ρ = , 800Q = . We define MSEσ as the factor to

evaluate the degree of the approximation between treemult and the theoretical optimum counterpart.

optim optim

[1,K ]

( ) ( ) ( ) ( )

( )|d d |/(d * K * | |)MSE S

v v v v

V vv st

n t

Vσ∈ ∈

= −∑ ∑ (15)

where ( )d vt is actual tht -hop distance and | |SV denotes the

number of sensors in Vs . The better the degree of the approximation between actual routing and the theoretical model, the less the total energy cost will be. The percentage of deviation is compared among classical geographic-aided routing GPRS, Minimum Energy Consumption routing, MEC[13], greedy algorithm[14] and TORA with respect to MSEσ . As shown in Fig.1, the deviation from TORA always keeps the smallest value compared to the rest of other schemes with the increase of node’s density, which denotes that TORA performs better than other schemes according to the realization of minimal total energy-cost level in networks, because of the prior theoretical results being adopted to the design of heuristic factor in TORA.

50 60 70 80 90 100 110 120 130 1400

0.05

0.1

0.15

0.2

0.25

0.3

Node Density

Per

cent

age

of d

evia

tion

Greedy

MECGPRS

TORA

Figure 1. Fitting degree to theoretical optimal structure Energy balance analysis is shown in Fig. 2 at the node level

after 80 times of transmission-operations. In annular domain with center at sink and radius r ∈[5,10], we randomly select 40 deployed sensors for energy-status observation by using different routing algorithms. The peak values of each curve in Fig. 2 are corresponding to normalized remaining energy level. Simulation results show that the average level of TORA is higher than the other two algorithms(GPRS and MEC) for the reason that the adaptive ant-agents mode has been introduced into TORA.

5 10 15 20 25 30 350.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

Node ID

Rem

aini

ng e

nerg

y le

vel/

Initi

al e

nerg

y le

vel

TORA

MECGPRS

Figure 2. Comparison of remaining energy level

Within the average delay is restricted below scheduled delay constraint, which is set as 8ms in the simulation. Fig. 3 illustrates the mean of end-to-end delay comparison and the average delay of TORA is less than MEC and GPRS, that is benefited by the updating pheromone rule (14) based on delay constraint to reinforce the trails on optimal path and weaken the trails on those bad ones .

4 5 6 7 8 9 10 110

1

2

3

4

5

6

Transmission rate

End

to

end

dela

y (m

s)

MECGPRSTORA

Figure 3. End-to-end packet delay

V. CONCLUSION For constructing optimal routing structure in WSN, it is

important to minimize the total energy cost of data transfer from the data-collecting region to a fixed sink with delay constraint of QoS, meanwhile, to improve the energy robustness of routing tree structure in order to reduce the probability of disconnected subnets, which is caused by unreasonable energy distribution on sensors in data-gathering routing structure. The paper presents an optimal algorithm based on ACO, i.e., TORA to achieve the above two important objectives. Via dividing the WSN into different kinds of functional regions, the energy consumption of each sensor can be roughly estimated in advance. The novel design of heuristic factor construction and pheromone updating rule can endow artificial ants the ability to adaptively detect the local energy status in WSN and intelligently approach the prior theoretic model in the process of routing construction. Finally, the proposed optimal routing tree can improve the energy efficiency and robustness of WSN in data gathering.

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